Exp Astron (2013) 35:507–526
DOI 10.1007/s10686-012-9320-3
ORIGINAL ARTICLE

Measurement of arrival time of particles
in extensive air showers using TDC32
S. K. Gupta · J. Christiansen · Y. Hayashi ·A. Jain · P. K. Mohanty · K. C. Ravindran ·B. Satyanarayana

Received: 1 August 2012 / Accepted: 26 September 2012 / Published online: 13 October 2012
© Springer Science+Business Media Dordrecht 2012

Abstract Arrival time of particles in an extensive air shower (EAS) is a key
physical parameter to determine its direction. EAS direction is useful forstudies of anisotropy and composition of cosmic rays, and search for multiTeV γ -rays sources. Accurate timing may be used to search exotic phenomena
such as production of new particles at extremely high energies available during
early stages of development of EAS and also for detecting sub-relativistic
hadrons in EAS. Time to digital converters (TDCs) are used to perform
this task. Traditional TDCs operate in the START-STOP mode with limited
dynamic range and single-hit capability. With the advent of high luminosity
collider LHC, need for TDCs with large dynamic range, multi-hit capability
and TRIGGERED mode of operation became necessary. A 32 channel TDC
was designed for the GRAPES-3 experiment on a CAMAC platform around
TDC32, an ASIC developed by micro-electronics group at CERN, Geneva.
Four modules were operated in the GRAPES-3 experiment. Here, we present
details of the circuit design and their performance over several years. The
multi-hit feature of this device was used to study the time structure of particles
in the EAS on time scale of ∼1 μs. The distribution of time intervals in the

S. K. Gupta · A. Jain · P. K. Mohanty · K. C. Ravindran · B. Satyanarayana
Tata Institute of Fundamental Research, Mumbai 400 005, India
S. K. Gupta (B) · A. Jain · P. K. Mohanty · K. C. Ravindran · B. Satyanarayana
GRAPES–3 Experiment, Cosmic Ray Laboratory, Ooty 643 001, Indiae-mail: gupta@grapes.tifr.res.in
J. Christiansen
Microelectronics Group, CERN, Geneva 23, Switzerland
Y. Hayashi
Faculty of Science, Osaka City University, Osaka 558-8585, Japan508

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multi-hit data shows an exponential profile with a time constant of ∼370 ns.
These delayed particles are likely to be neutrons produced in the EAS corethat were recorded in the scintillator detectors following the relativistic EAS
front.
Keywords Cosmic rays · Extensive air showers

1 Introduction
An overwhelming fraction of the high energy cosmic rays are charged particles
that are deflected by interstellar magnetic fields during their propagation in thegalaxy. The random orientation of galactic magnetic field effectively converts
the motion of cosmic rays into diffusion. This results in a total loss of information on the direction their sources. Thus, the only option available to directly
identify the cosmic ray sources is to detect the photon (γ -ray) component
that travels in a straight line, unaffected by interstellar magnetic fields andthus preserving the source direction. Therefore, important knowledge of highenergy processes leading to production and acceleration of cosmic rays to highenergies may be obtained through the detection of cosmic γ -rays.
A large fraction of cosmic rays of energies below the ‘knee’ are accelerated
in supernovae explosions within the galaxy, mainly through diffusive shock
acceleration [1]. This makes supernova remnants in the galaxy an important
target for detection of high energy γ -rays. Pulsars are also capable of accelerating particles to high energies [2]. The CRAB pulsar and its nebula have been
extensively studied at most wavelengths and the observations by satellite based
detectors have established it as a standard candle from MeV to GeV energies.
These observations imply the presence of highly relativistic electrons thathave been accelerated to energies beyond hundreds of GeV. The existence ofsynchronous pulsed emission from radio (10−5 eV) to GeV γ -rays, underlines
the importance of the CRAB pulsar in accelerating charged particles in the
nebula [3].
Study of photon sources above 100 GeV requires large collection area andexposure time, that are presently possible only with ground based detectors
employing the atmospheric Cherenkov technique (ACT) [3, 4]. However, thecosmic sources of yet higher energy (≥10 TeV) γ -rays can only be studied using
the extensive air shower (EAS) technique, that allows sufficiently large areaand exposure time factors. Since the γ -ray flux from a source has to be detectedagainst a massive background contributed by the isotropic flux of cosmic rays,
the success of this technique critically depends on an effective rejection ofthis massive background. For a point source, the signal to background ratio
is inversely proportional to the square of the angular resolution. Therefore,
the most critical parameter in an EAS detector system is its angular resolution.
The technique of relative arrival time has been widely used in EAS arrays fordetermining the arrival direction of showers [4–7].

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Study of EAS at energies below 100 TeV involves detection of showerelectrons that suffer significant scattering in the atmosphere, prior to detection
at ground level. Therefore, the angular resolution attainable in an EAS arrayis relatively poor as compared to an ACT that detects Cherenkov photons.
Furthermore, the angular resolution of an EAS array also depends on theshower size at detection level and improves with increasing shower size. The
best possible angular resolution may be achieved by deploying a carpet ofdetectors to maximize detected number of EAS particles and MILAGROand ARGO-YBJ experiments are examples of this approach. The MILAGRO
experiment had instrumented a 8 m deep water pond of 80 × 60 m2 area,
to detect Cherenkov photons produced by EAS particles inside water byphotomultipliers (PMTs) [8]. The ARGO-YBJ experiment detects particles
by a carpet of resistive plate chambers, covering an area of 74×78 m2 [9]. Since
the total carpet area in both experiments is < 6000 m2 , hence the sensitivity ofthese experiments peaks below 5 TeV.
In an alternative approach, the angular resolution may be improved bydecreasing the inter-detector separation in an array. This strategy provides
a reasonable compromise between a small area carpet array and a large
area sparsely instrumented array. However, practical constraints imposedby logistical and funding considerations limit the total number of detectors
deployed in an array. Further, an array provides only a sampling of particle
density in an EAS. For example, in the Tibet ASγ [10], CASA-MIA [11], EASTOP [12], KASCADE [13], GAMMA [14] arrays, the physical area covered
by detectors is ≤1 % of the total area of the array. The fraction of physicalarea covered by detectors in an array is a key factor that determines theangular resolution, which is critically important in search of γ -rays at multiTeV energies. With these definitive considerations in mind, the GRAPES3 (Gamma Ray Astronomy at PeV EnergyS Phase-3) was designed to haveone of the most compact configuration in a conventional EAS array, with aseparation of only 8 m between adjacent detectors. The GRAPES-3 detectors
are deployed in a symmetric hexagonal geometry, with a coverage of ∼2 % of
total area of the array [7, 15].
The energy dependent angular resolution and the absolute pointing accuracy of the GRAPES-3 array was measured using three different methods that
included, the even-odd, left-right and the Moon shadow technique. The evenodd method provides a quantitative estimate of the best achievable angularresolution as a function of shower size. The left-right method provides a measure of the shower front curvature and also serves as an independent measureof the angular resolution. In the third method four years of observations
were used to obtain the shadow of Moon at a significance level of ∼5σ . The
Moon shadow besides providing an estimate of the angular resolution. Being
caused by a celestial object it also yielded the absolute pointing accuracy of
the array. Nearly identical values of the energy dependent angular resolution
obtained by these three independent techniques indicates the reliability ofthese measurements. The angular resolution of the GRAPES-3 array is 1.4◦
at 10 TeV that steadily improves to 0.5◦ at 80 TeV [7].

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For an incident EAS, the shower particles reach a given detector at a time,
based on detector location and the EAS direction. For an EAS traveling along
a direction θ, φ, the particles reach the detector located at r at a time r.n/c,
relative to the origin of the co-ordinate frame. Here, the unit vector n is along
θ, φ and the velocity of EAS particles was assumed to be the velocity of lightc. Thus, in principle, if the arrival times at a minimum of three detectors
were known, the unknown EAS direction (θ, φ) could be obtained from thearrival time data. The error in the measurement of arrival angle θ ∼ ct/d,
where t is the error in time and d is the inter-detector distance. Therefore,
accurate measurement of time is critically important for obtaining a goodangular resolution. A time to digital converter (TDC) serves as the basic device
that measures the arrival time of particles in each detector relative to the EAS
trigger.
In addition, the TDCs with a multi-hit capability may be used to study thetime structure of particles in the shower front. The shower front primarily
comprises of relativistic particles that includes leptons and hadrons travelingat nearly the velocity of light. However, the neutrons produced in the shower
core, being electrically neutral and possessing a very long lifetime (882 s)
can travel large distances even at relatively low energies of ∼ sub-GeV. The
presence of such sub-relativistic neutrons as a potential source of delayedparticles in the EAS was anticipated a long time back [16]. The first indicationof neutrons being the particles delayed by several μs relative to the EAS
front came from some of the early experiments [17]. Recent measurements ondelayed neutrons in the EAS have been extensively discussed in [18]. Using thedata from neutron monitors operated along with the Tien-Shan array presenceof delayed neutrons was reported with delays ranging from hundreds of μs toseveral ms possibly due to thermalization during the detection process [19].
However, the neutrons produced in the atmosphere follow the EAS front withdelays of only a few μs. The detection of neutrons offers another independent
method to identify the hadronic nature of the primary particle that may be
used for a better hadron to γ separation.
The GRAPES-3 experiment consists of a dense array of plastic scintillator
detectors and a large area tracking muon detector. The array at present
consists of about 400 plastic scintillator detectors (each 1 m2 ). These detectors
are deployed with an inter-detector separation of 8 m. The array is being
operated at Ooty in India (11.4◦ N, 76.7◦ E, 2200 m altitude) [15]. The total
area of tracking muon detector is 560 m2 with an energy threshold of 1 GeV in
the vertical direction [20]. In Section 2 the operational characteristics of someof the conventional TDCs and that of the TDC32 are discussed. In Section 3
a brief description of the CAMAC printed circuit board designed to house
the TDC32 is given. The performance of two commercially available TDCs,
namely, Phillips Scientific of USA and Hoshin of Japan alongside TDC32
are compared in Section 4. The measurements of the time distribution ofdelayed particles are summarized in Section 5. The conclusions of this study
are presented in Section 6.

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2 Time to digital converters
A TDC is used to measure the time interval between two digital pulses by
converting it into a numerical count that may be stored and accessed for further
analysis. Since, each scintillator detector in GRAPES-3 experiment measures
the arrival time of particles in an EAS, a large number of TDC channels are
required to perform this task. This requirement could, in principle, be met ina cost effective manner by employing TDC32. The TDC32 is an application
specific integrated circuit (ASIC) that contains 32 channels and was developedby Microelectronics group at CERN, Geneva as a prototype TDC for the LHC
experiments. Some of the unique capabilities of this ASIC include a large
dynamic range, multi-hit, low latency, excellent stability and the flexibility
to use different operational modes, including the START-STOP and TRIGGERED modes. TDC32 is programmed using standard JTAG protocol andvarious operational parameters can be easily changed as per the requirementsof the experiment [21]. TDC32 achieves a resolution of 521 ps with a clock of
60 MHz. This resolution is perfectly suitable for the GRAPES-3 experiment,
where shower particles are spread several ns in time.
Conventional TDCs available commercially, for example, LeCroy, USA[22], Phillips Scientific, USA [23] or Hoshin, Japan [24] generally operate in
the START-STOP mode. This entails the generation of a common START(STOP) signal that must precede (follow) the signals to be measured. Thatin turn, necessitates the use of long delay cables to ensure a proper temporalsequencing of signals. The dynamic range of most of these TDCs is limited to
12 bits and their operation confined to the single-hit mode. Therefore, once achannel receives signal it stays dead until the data is read and/or cleared. Thisis a serious limitation, specially in high rate and/or noisy environments where
even an unwanted/noise pulse arriving before the signal can result in the lossof real signal. Most of these commercial TDC modules also contain far fewer(8 or 16) channels than the TDC32.
The eight channel LeCroy TDC (model 2228A) employs Wilkinson rundown method to convert a time interval into charge by charging a capacitor
using a constant current source for the duration of the time interval being
measured. Thereafter, the stored charge is digitized [22]. The Phillips Scientific
TDC (model 7186) implements 16 channels of time to amplitude conversion
followed by a digitization section and CAMAC interface in a single width
CAMAC module [23]. Phillips Scientific [23] and Hoshin [24] TDCs use thetechnique of successive approximation for digitization, resulting in a non-linear
response as discussed later on in Section 4. Unfortunately, these TDCs also
suffer from a rather high power consumption (0.1–1 W per channel), highlatency because of slower conversion and in some cases the time resolution
gets modified in the presence of magnetic field [25].
The availability of TDC32 with 32 channels offers a great opportunity todevelop a TDC system that is relatively inexpensive and offers numerous
advantages over the earlier commercial models. These advantages include, a512

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large dynamic range of 21 bits, multi-hit capability with a double-hit resolutionof 15 ns, operation in both START-STOP and TRIGGERED modes, a low
power consumption (∼10 mW per channel) and low latency. TDC32 works onan entirely different mechanism of time division with the help of an external
clock of maximum frequency of 60 MHz. The corresponding time period of
16.67 ns is effectively divided by a factor of 32, resulting in a resolution of
16.67/32 = 0.52 ns per count. The enhanced resolution is achieved with theaid of a chain of 32 delay elements that form a delay locked loop (DLL)[26, 27], where the basic frequency remains unchanged, but the phase is shiftedusing a delay element. The implementation of the DLL was achieved by using
standard CMOS technology.
The DLL for the TDC32 contains 32 identical delay elements, a phasecomparator and a charge pump. The input to the DLL is a 60 MHz clock. The
delay of each element can be adjusted by a control voltage. In the locked state,
the 32 elements in the loop produce 32 outputs of 60 MHz, that are delayed byan equal amount by successive elements, such that the total delay in the loop
equals one clock period. The phase detector compares the phase between the
60 MHz input clock with the output at the end of the loop and adjusts the pumpby changing the bias of each delay element by an identical amount to ensurethat the total delay stays equal to one clock period. Thus, the DLL effectively
divides one clock period into 32 equal parts. This information is encoded into
5 bits that are combined with the 16 bit coarse count to provide a 21 bit output.
The jitter in time after reaching the locked state was minimized through acareful design effort, because a large jitter can effectively compromise theperformance of the TDC. A finite amount of time is needed for the delay chain
to reach a locked state. This time depends on the current used in the charge
pump. A low current results in a longer time to reach the locked state, butleads to smaller jitter. On the other hand a higher current leads to a faster lockwith larger jitter. The current for the charge pump may be controlled througha JTAG command [21].

3 CAMAC printed circuit board for mounting TDC32
The time resolution and offset in a conventional TDC such as the Phillips
model 7186 or Hoshin model C021 tend to drift with time and also varyfrom channel to channel. Hence these TDCs have to be calibrated at regularintervals to measure this variation. For TDC32, the time resolution depends
only on the stability of the 60 MHz clock and all 32 channels, in general,
have an identical resolution. Both Hoshin and Philips TDCs possess a time
resolution better than TDC32, but their dynamic range is very limited. In
conventional TDCs, if multiple STOP signals arrive after the START, then
only the first STOP is registered. But the TDC32 is capable of measuring timeinterval between a START and multiple STOPs. In TRIGGERED mode the
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for START inputs. The advantage of this mode is that the long delay cablerequired in START-STOP mode for every detector is avoided. The TDC32
may be programmed using standard JTAG protocol to operate in different
modes unlike the conventional TDCs.
In TDC32 the input and control signals utilize a TTL logic. Depending upon
the needs to the experiment, the TDC32 may be programmed to write the data
for the channels hit or for every channel. The data contain a 5-bit channel
number and 21 bits of time information. The TDC32 may be programmed toprovide data after subtracting the time of common START. If multiple hits
occur, then the time of each hit is written in the event buffer along with thecorresponding channel number. In the TRIGGERED mode, after an event ofinterest is identified, the time of occurrence prior to, or after the trigger canbe recorded. This is accomplished by programming the TDC32 to search forevents during a time window before or after the START pulse.
In general, electronic instrumentation used for particle detection involves
measurement, control and data recording. A modular system that is compact,
flexible, and operates at high speeds through a digital interface is highly
desirable. The CAMAC (Computer Automated Measurement and Control)
is an open-architecture IEEE standard 583 that is non-proprietary and usedworldwide. CAMAC incorporates an easy to implement mechanical andelectrical specifications. One TDC32 ASIC was mounted on a printed circuitboard (PCB) placed inside a double width CAMAC module, hereafter called‘G3TDC’ module. The CAMAC DATAWAY powers the G3TDC moduleand also serves to address, control and bus the data using standard CAMAC
commands. The benefits of this modular design include compactness, easy
replacement of faulty modules and the flexibility to upgrade the design infuture. The choice of CAMAC was dictated by its widespread use in the
GRAPES-3 data acquisition system (DAQ). The station number, selected byan on-board DIP switch, indicates the location of a given G3TDC modulein a crate, the address lines differentiate between channels and the function
code performs specific operations including the READ, WRITE, CLEAR etc.
The data from each channel are read into the controller during the READ
operation and then stored in a memory buffer interfaced to the data storage
computer.
The TTL logic is used for control and input/output operations since the
TDC32 also utilizes this logic for various operations. Since most of thecontrol electronics in the GRAPES-3 experiment is also based on TTL, its
implementation in G3TDC posed no problems. The JTAG signals used toprogram the TDC32 after the power is switched on, are differential TTL,
because these signals have to drive a relatively long cable (∼4 m), they areconverted into normal TTL, just before programming the TDC32. Similarly,
the output signals from TDC32 drive TTL buffers en-route to the CAMAC
controller. The control signals for the output buffers are generated in thecontrol circuit segment of the PCB. A provision was made to daisy chain
the JTAG programming signals from one to the next board for the ease of
programming a number of G3TDC modules.

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A two layer PCB was designed for mounting the TDC32 in a CAMAC
module. The PCB houses, one TDC32 (84 pin PLCC), one Isplsi-PAL (32pin PLCC) and a few additional ICs. In view of the presence of a relatively
high frequency (60 MHz) clock, the layout of the components and the routingof the tracks was carried out with considerable care, specially since the highfrequency clock can generate ripples on the power lines that can adversely
impact the operation of TDC32. A separate +5 V isolated supply was provided
on the PCB along with decoupling capacitors for each IC. 50 impedance RG174 co-axial cables were used to propagate the 60 MHz clock and the shield in
the co-axial cable was grounded to minimize potential electrical interferences.
The 32 inputs of TDC32 were fed via 64 pins of two FRC connectors mounted
on the front panel of the G3TDC module. These signals carry arrival time
information of particles in a detector. The routing of STOP signals to the input
buffer leading into TDC32 was done by maintaining similar track lengths tominimize potential time offsets in the PCB. A majority of the tracks wererouted on the solder side and the unused area on the component side wascovered with ground plane to further reduce the electrical noise.
Functionally, a G3TDC module consists of one TDC32 as the core component, a CONTROL UNIT, INPUT BUFFER, OUTPUT LATCH and a
JTAG interface. A block diagram of G3TDC module is shown in Fig. 1. Afterthe power is switched on, the JTAG interface programs the TDC32 and that
includes the selection of, (i) the operating mode (TRIGGER or STARTSTOP), (ii) rising or falling edge of signal for timing, (iii) enable and/or disable

LATCH_DATAENABLE_DATACAMAC Commands

SCAN Clock
60 MHz Clock

CONTROLUNIT

TRIGGERSTARTOUTPUT CAMAC Data Bus
LATCH
TDC Data Bus

CLOCK
TRIGGERSTARTGET_DATADATA_READYSTOPS (32)
From Detectors

JTAG SIGNALSINPUTBUFFERCHANNEL (1:32)

JTAG
INTERFACE

TDC32 SETUP/CONTROL

Fig. 1 Block Diagram of CAMAC based G3TDC

TDC 32
TCK
TDI
TDO
TRST

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specific channels and so on. The JTAG setup functions are executed throughfour lines, namely, TCK (clock), TDI (input), TDO (output) and TRST (reset)
as shown in Fig. 1. The CONTROL unit provides the interface with theexternal world and controls the access for reading the TDC32 data. The
TDC32 receives the TRIGGER or START through the CONTROL UNIT
that also inputs 60 MHz clock for the conversion of data in enabled channels.
The STOP pulses from the GRAPES-3 detectors are buffered through the
INPUT BUFFER into the TDC32 and upon the receipt of the TRIGGER thedata are latched and loaded into the OUTPUT LATCH, after due handshake
involving GET_DATA and DATA_READY commands. A command fromthe CAMAC controller initiates the transfer of the latched data into the
CAMAC bus, by making use of the 1 MHz GRAPES-3 DAQ SCAN clock.
Once the data are processed by the TDC32, then a DATA_READY signal isset to HIGH state indicating that the data are ready to be read from the 256
byte internal buffer of the TDC32.
The entire operation of the CONTROL UNIT is implementing by a careful
sequencing of various steps with the aid of an elegant and simple hardwired
logic using only seven flip flops, hereafter called FF1 through FF7, and a
few basic gates as shown in Fig. 2. The SCAN clock is propagated when the
CAMAC station housing a G3TDC module is enabled through an N_LINE.
The change of state of various FFs due to passage of SCAN clock resultsin the generation of timing waveforms as shown in Fig. 3. The operation of
the CONTROL UNIT may be understood by a closer examination of Fig. 2
in conjunction with Fig. 3. The rising edge of the SCAN clock sets FF1,
alternatively to HIGH and LOW states, every 1 μs, as seen from the twocomplementary waveforms i.e. the 3rd and 4th from top in Fig. 3. The data
for each channel contains a total of 32 bits (21 = 16 coarse + 5 fine bits

EN_RD1

N_LINE

D

_
Q

H

D

Q

D

1 MHz

Q

D

Q

D

Q

Q

EN_RD2LATCH

MONOSHOT

60 MHz
CLOCK

D

Q

_
Q

GET_DATA
D_
Q

Fig. 2 Schematic of the control logic for G3TDC

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CAMAC
N LINE

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1

2

3

4

5

SCAN
1 MHz
FF1 Q
FF1 Q

FF2 Q
FF3 D
FF4 D
FF3 Q
FF6 D
FF5 Q
60 MHz
FF7 D
FF6 Q
FF7 Q
GET_DATA
LATCH

Fig. 3 Timing diagram for control logic of G3TDC

of time information, 6 bits for addressing a channel, 5 bits for addressing
different modules) that are read as two 16 bit packets by the GRAPES-3 DAQ.
This task is accomplished by using complementary outputs of FF1, named,
EN_RD1 and EN_RD2, respectively, as shown in Fig. 2. The second SCAN
clock also sets FF2 to a HIGH state for the duration of READ operation.
The combination of remaining FFs and AND gates shown in Fig. 2, generates
a GET_DATA signal that is synchronous with the trailing edge of 60 MHz
clock, as shown by the 2nd waveform from bottom in Fig. 3. However, theleading edge of GET_DATA precedes 60 MHz clock without overlappingwith the previous pulse in the train of 60 MHz pulses. This was the mostcritical requirement in the CONTROL UNIT, since the available time window
was only 8.3 ns. A LATCH signal is generated immediately following the
GET_DATA as shown by bottom waveform in Fig. 3, thus ensuring that thecorrect value of time is latched and recorded by the DAQ.

4 Comparative performance of TDCs
The G3TDC modules were extensively tested and calibrated prior to installation in the GRAPES-3 DAQ. Initially, the signals from several detectors wereconnected in parallel to the G3TDC as well as the Phillips or Hoshin TDCs forExp Astron (2013) 35:507–526

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a comparative field study of their performances. For the present study we haveused six 16-channel TDC modules, each from Phillips and Hoshin for a total of
96 channels from the two manufacturer. We also used three G3TDC modules
for a total of 96 channels.
It was observed that the time resolution (ps) of commercial TDCs displayed
significant channel-to-channel variation and for some of the channels it also
varied with time. To correct for these variations, a multi-channel calibration
system was designed to measure the time resolution (TR) of individual channels in each TDC module. The calibration system employs six quartz crystal
oscillators to provide stable clocks of known frequency. The 1st pulse in thepulse train was used as the START and the 2nd as STOP, for each channel in
the TDC module being calibrated. Therefore, the time interval between thesetwo pulses was ‘T’, where T is period of the oscillator. This procedure wasrepeated a hundred times. Thereafter, the 3rd, 4th, . . ., nth pulse, respectively,
were used as STOPs, again repeated a hundred times for each delay. Thus, each
TDC channel was calibrated a hundred times for the time intervals of T, 2T,
3T, . . ., nT. The six quartz crystals oscillators of frequencies 10, 16, 20, 25, 32,
and 40 MHz were used. Typically ∼140 distinct time intervals were recorded
during this calibration exercise over a time window of 1000 ns, thus ensuring areasonably uniform coverage of this window.
As mentioned earlier, a total of three G3TDC, six Phillips and six Hoshin
modules were used in the present study, amounting to a total of 96 channels foreach of the three TDC types. The calibration results for one out of 96 channels
from each of the three TDC types are shown in Fig. 4. The result from theG3TDC is shown in the top panel and a linear fit to this data yields a TR of
520.88 ps. Results from the Phillips and Hoshin TDCs are shown in middle andbottom panels, respectively in the same figure. A linear fit to data yield TRs of
199.8 and 285.2 ps for Phillips and Hoshin TDCs, respectively.
Next, the time difference between the measured delay and the linear fit wascalculated. This time difference termed ‘deviation’ and represented by ‘t’is shown as a function of delay in Fig. 5a for the G3TDC channel shown in
Fig. 4a. The values of the t are uniformly distributed around a null mean.
The root mean square (rms) t termed ‘trms ’ is 82 ps. The deviation forPhillips channel is shown in Fig. 5b. Here, a large and systematic departurefrom linearity as a function of delay is observed. This behavior is seen in all
Phillips channels that display a concave profile, although the actual magnitudevaries from channel to channel. trms = 603 ps is calculated from the data
shown in Fig. 5b. The Hoshin channel also showed a fairly large systematic
non-linearity with a convex profile as shown in Fig. 5c and trms = 298 ps.
Next, we generated three distributions of TRs for each of the three TDC
types separately, to get a measure of the spread in their magnitudes. These
distributions were fitted to a Gaussian function and the fit parameters including the mean and standard deviation (SD) are shown in Table 1. The mean
TR was 520.854 ps for the G3TDC, 199.52 ps for Phillips and 282.7 ps for518

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Fig. 4 Typical TDC
calibration for, a TDC32 time
resolution (TR) = 520.86 ps,b Phillips TR = 199.8 ps,c Hoshin TR = 285.2 ps

2000

(a)
1500

1000

500

TDC32
4000

(b)
Counts

3000

2000

1000

Phillips
3000

(c)

2000

1000

Hoshin
0

200

400

600

800

1000

Time (ns)

Hoshin TDCs. On the other hand, the magnitudes of SD for these three TDCs
are radically different from each other and therefore, a somewhat unusual
method for plotting these distributions was adopted. The minimum value ofeach distribution was adjusted to 1.2 ps by adding an appropriate offset. This
procedure allowed all three distributions to be accommodated in the same
panel, while using a log-log scale as shown in Fig. 6. The data are represented
by the histograms and the Gaussian fit by dashed curves. Due to the proceduredescribed above, the X-axis labeled in picoseconds does not represent the true
mean of the distribution, however, the width does correspond to the data.
Since, only the channel-to-channel variations are being investigated here, theabove log-log representation indeed serves this limited purpose.
The narrowest histogram labeled ‘a’ corresponds to a TR of 96 G3TDC
channels and a Gaussian fits the data rather well as seen from Fig. 6. The
measured TR was 520.854 (Table 1) as against an expected value of 520.833 ps
based on a frequency of 60 MHz. The small difference of four parts in 105 in thevalues of the measured and expected TRs is consistent with the accuracy of theExp Astron (2013) 35:507–526

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Fig. 5 Deviation fromlinearity obtained using TDC
calibration for, a TDC32
trms = 82 ps, b Phillips
trms = 603 ps, c Hoshintrms = 298 ps

1

(a)

TDC32

(b)

Phillips(c)

Hoshin0Δt (ns)

1

0

1

0

0

200

400
600
Time (ns)

800

1000

frequencies of quartz oscillators used. Furthermore, TR of G3TDC channels
are nearly constant as indicated by a SD of only 14 fs. In contrast the Phillips
TDCs with a mean TR of 199.52 ps had a large spread with SD = 440 fs, nearly∼30 times larger than the G3TDC (see Table 1), as seen from the plot labeled‘b’ in Fig. 6. Finally, the Hoshin TDCs displayed the largest spread in TR witha mean of 282.7 ps (see Table 1) and SD = 3600 fs, nearly ∼260 times larger
than the G3TDC, as shown by plot labeled ‘c’ in Fig. 6. Therefore, these studies
clearly establish that the performance of G3TDC in reliably measuring thetime is vastly superior than the two commercial TDCs studied here.

Table 1 TDC parameters

TDC type

Mean (ps)

S.D. (fs)

G3TDC
Phillips
Hoshin520.854199.52
282.7

14
440
3600

520

(a)

30

No. of TDC channels

Fig. 6 Distributions of TDC
time resolutions after setting
mean = 1.2 ps. Histograms
are for 96 channels anddashed curves are Gaussianfits for, a G3TDC, σ = 14 fs,
b Phillips, σ = 440 fs, c
Hoshin, σ = 3600 fs

Exp Astron (2013) 35:507–526

σ = 14 fs(b)
σ = 440 fs(c)
σ = 3600 fs

10

3

1

3

10

20

picosecond

According to the technical specifications, TDC32 has an rms time resolutionof 0.2 ns, when operated at 60 MHz. However, in the START-STOP mode
employed here, the measured time was obtained as a difference between a
START and a STOP signal. Therefore, the effective rms time resolution is the
0.5
quadratic sum of the two individual resolutions, (0.22 + 0.22 ) = 0.28 ns. The
calibration data for a fixed delay for hundred events was used to generate a
distribution of the TDC counts that is shown as a histogram in Fig. 7, after
subtracting the mean of the TDC counts to center the distribution at zero.
The rms width of this histogram is 0.49 counts and a Gaussian fit yields anearly identical SD of 0.48 counts. Using a TR of 0.521 ns for the TDC32,
yields an rms time resolution of 0.49 × 0.521 = 0.26 ns, in close agreementwith the expected magnitude of 0.28 ns. Thus, we conclude that the G3TDC
has performed exactly according to the technical specifications [21].

Fig. 7 Distribution of TDC
counts for a fixed delay for
100 events, a histogram
G3TDC data, rms = 0.49, b
Gaussian fit, SD = 0.48

80

Events

60

40

20

0

-4

-2

0
2
TDC Counts

4Exp Astron (2013) 35:507–526

521

5 Time distribution of EAS particles
The TDC32 was designed with a built-in multi-hit capability and a double-hit
resolution of only 15 ns as outlined in Section 2 [21]. In the discussions above,the multi-hit feature of this device was not explored. Here, this capability is
exploited to measure the temporal structure of the particles in the EAS, and its
dependence on the distance from the core. Nsum is defined as a sum of particles
recorded in every GRAPES-3 detector triggered. Here the detector receiving
a signal ≥40 % of a minimum ionizing particle with arrival time informationfrom associated TDC channel is considered triggered for this purpose. Nsum
turns out to be a good proxy for the primary energy of the EAS as shown
below.
A total of 4.26 × 108 showers, recorded from January 1 to June 30, 2010
were analyzed. Only the EAS that triggered a minimum of 10 detectors wereused for further analysis. An approximate position of the EAS core Rc wasevaluated from the weighted mean of the locations ri of the seven detectors
with highest particle densities ni , labeled H7 , whose weights equaled thedensities in respective detectors as described in [28].
H ni ri(1)
Rc =  7
H7 ni
The scintillator detectors in the GRAPES-3 array are shown as blue points
in Fig. 8. A cut was applied on the location of the EAS core, to restrict it within
an area that excluded a minimum of two outermost rings of detectors. The
footprints of the cores of selected EAS are shown as red points. A total of
3.77 × 108 EAS, spread over an area of 1.27 × 104 m2 survived this cut, during
Fig. 8 The distribution of thecores of selected EAS
incident on the GRAPES-3
array

80
60

Y (m)

40
20
0
-20
-40
-60
-80

-120 -100 -80 -60 -40 -20

X (m)

0

20

40

60

80

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Exp Astron (2013) 35:507–526

a total live time of 160 d. The distribution of the number of EAS, ‘NEAS ’ witha particle sum of Nsum is shown as a histogram in Fig. 9, after multiplying by
N2.5
sum . Also shown on the same plot is a power law fit to the data in the range
50–3000 particles.
The frequency distribution of Nsum displays a power law behavior that may
be approximated to K × N−γ . Here, K is a constant, and γ = 2.58. This valueof 2.58 of spectral index may be compared with the values of 2.5 for the shower
size spectrum [28] and 2.56 ± 0.04 for the density spectrum of the particles in
EAS [29], measured earlier by us. The approximate equality of the spectral
indices from three different methods indicates Nsum to be a good proxy for the
primary energy of the EAS.
Next, we analyzed the multi-hit data from 106 detectors that were connectedto the four G3TDC modules in the GRAPES-3 DAQ. To transmit the signals
to the control room two different types of co-axial cables, namely, RG58
and 5D2V were used for 49 and 57 detectors, respectively. The transmission
properties of the 5D2V cable are superior than the RG58 cable. Therefore, thedata from 57 detectors that employ 5D2V cables were used for further analysis.
For each detector, the events containing double-hits during a programmed
window of 3000 ns were identified. The distribution of the time interval
between the two hits in a double-hit event for detector numbered 234 is shownin Fig. 10. The sharp peaks in this figure are a result of the reflections of
PMT signals in the 5D2V cable from detector 234 in the outdoor field to
the Fan-Out, and from the Fan-Out to the G3TDC module in the control
room. Next, we imposed a stringent cut on the level of reflection at <1.0 %,to select detectors for further analysis. Not surprisingly, only five out of 57
detectors passed this cut including detectors numbered, 199, 207, 230, 232 and234. The performance of a detector in the reconstruction of EAS direction isunaffected even by a much higher level of reflection, but this stringent cut was
imposed to analyze the double-hit data, that are far more sensitive to the levelof reflections.

1012

1011
2.5

NEAS X Nsum

Fig. 9 Distribution of
number of selected EAS
2.5 as‘NEAS ’ multiplied by Nsuma function of ‘Nsum ’. Fit todata shown as dashed line,−γ
yields NEAS = K × Nsum
where γ = 2.58

1010

109

108
10

10 2

N sum

103

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523

Fig. 10 Distribution of timeintervals of double-hit eventsin detector 234. Reflection
peaks are present at 500 and
2300 ns

60000

Events

50000
40000
30000
20000
10000
0

1000

2000

3000

Δt (ns)The double-hit events in these five detectors were further classified into
three categories, according to their distance from the shower core, namely, (a)0–50 m, (b) 50–100 m, and (c) >100 m. Next, the distribution of the double-hit
time intervals was obtained for the three ranges of core distances listed above.
Since the time distributions for a given core distance range were very similar
for all five detectors, their data were combined and are shown in Fig. 11. The
distribution of double-hit time interval of 6.8 × 106 events for core distance 0–
50 m is shown in Fig. 11a. The data were fitted with an exponential function
tand a constant background N = A + B exp(− τ ) , here N is number of events,
t time interval. τ , A, B are constants derived from the exponential fit.
In the GRAPES-3 DAQ, the discriminator outputs have a width of ∼150 ns
as may be seen from the absence of events below this value in Fig. 10. Thus,
the minimum recorded time interval always exceeds 150 ns. Since the width ofthe programmed window for G3TDC was set at 3000 ns, hence the maximum
time interval can not exceed this value. With the above two limiting conditions,the data in Fig. 11a were fitted to an exponential and a constant backgroundin the range 200–2700 ns. This yielded a time constant, τ = (363 ± 36) ns. The
distribution of time intervals for core distance of 50–100 m containing 3.4 × 106
events is shown in Fig. 11b. The data, when fitted to the same functional formin the range 200–2700 ns yielded a time constant, τ = (374 ± 28) ns. Similarly,
the distribution of events for core distances of >100 m containing 3.7 × 105
events is shown in Fig. 11c. This data, when subjected to the same fit gave atime constant, τ = (373 ± 37) ns. Thus, within the limits of the accuracy ofthese measurements (at levels of ∼10 %), the time distributions for the above
listed three distance ranges of EAS core appear to demonstrate very similar
exponential profiles.
As mentioned earlier, the presence of sub-relativistic neutrons in an EAS
could explain the delay profile observed in Fig. 11. In future, we plan tocarry out extensive Monte Carlo simulations of neutron production in the
EAS cores to obtain a significantly better understanding of their delay profile.

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Exp Astron (2013) 35:507–526

Fig. 11 Distribution of timeintervals of double-hit eventsfor core distance, a 0–50 m, b
50–100 m, c >100 m

200000(a)150000τ = (363+36)_
ns

100000

Number of Events (N)50000

100000(b)

50000

τ = (374+28)
_
ns

15000

(c)
10000

τ = (373+37)
_
ns
5000

500

1000 1500 2000

2500 3000

Δ t (ns)

These simulations would also focus on the observed weak dependence of thedelay profile on the distance from the core up to a maximum of 100 m. With
the planned upgrade of the GRAPES-3 array through the replacement of theremaining RG58 co-axial cables by vastly superior 5D2V cables and by using
the multi-hit G3TDCs to record the data from each detector, we expect todetect a sizable number of neutrons in these detectors. The measurement of
neutrons could potentially serve as an additional constraint on the modelsof hadronic interactions. It could also provide the GRAPES-3 array with an
added capability to discriminate against the hadronic showers while searchingfor multi-TeV γ -rays from discrete sources.

6 Conclusions
A time to digital converter ‘G3TDC’ built on a CAMAC platform using the
ASIC ‘TDC32’ developed at CERN has been subjected to extensive field tests
over several years in the GRAPES-3 experiment at Ooty. The results of these

Exp Astron (2013) 35:507–526

525

tests show that this device performed exactly as was originally designed. It also
displayed exceptional long-term stability and negligible channel-to-channel
variation in terms of time resolution. It was successfully operated in the
TRIGGERED mode with a programmable window of 3000 ns. The analysisof the EAS data showed that small levels of reflections during transmission of
signals over long co-axial cables could be easily detected. The multi-hit featureof this device could be used to measure the time structure of delayed particles
in the EAS. This study clearly showed the presence of delayed neutrons that
display an exponential profile with a time constant of about 370 ns. These
neutrons could be detected following the passage of fast particles in the EAS
front inside the same detector. Such detection offers the promising possibilityof using neutrons for a better understanding of the hadronic interactions andpossibly improving the capability for the detection of multi TeV γ -ray sources.
Acknowledgements We acknowledge the outstanding contributions of K. Manjunath and C.
Ravindran in wiring, testing and installation of the G3TDC modules. We thank G.P. Francis,
V. Jeyakumar, and K. Ramadass for their timely help in the fabrication of several mechanicalcomponents used and for the assembly of these modules. We also thanks P.K Nayak for his
extensive help during the preparation of this manuscript. Stimulating discussions with S.R. Dugad
deserve a special mention. This work is dedicated to the memory of our brilliant colleague, late S.
Karthikeyan, who had made significant contributions to this as well as several other GRAPES-3
activities, prior to his tragic demise in a road accident.

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